- #1
B3NR4Y
Gold Member
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Homework Statement
An intensity current I descends down the z-axis from [itex]z = \infty[/itex] to z = 0, where
it spreads out in an isotropic way on the plane z = 0. Compute the magnetic field.
Homework Equations
The only relevant equation I can think of is Ampere's Law, [itex]\oint_\gamma \vec{B} \cdot d\vec{\ell} = \mu_0 I_{enc}[/itex]
The Attempt at a Solution
I think I should break up the problem into two parts. One to find the field due to the wire and the other to find the field due to the plane. The sum of these two will give me the total field, which is what I want.
For the wire I think the field is given by half of the field from an infinite wire. So we have that [itex]\vec{B}=\frac{\mu_0 I}{4\pi s} \hat{\phi}[/itex], but I'm not sure how this looks below the plane. I'm fine with this being the field everywhere else.
For the plane I'm not even sure how to think about it. It expands isotropically so I assume that [itex]\vec{K} = \frac{I}{r^2} \hat{r}[/itex] however I don't quite know how I will then deal with the plane to compute the field. I think I should use Ampere's law with a rectangular loop that encloses some of the above part of the plane and some of the below, but I get confused when computing it.
Thanks for any help